justanotherparadox / combinatorics

Open thinking is highly appreciated and break the learning curve only when you possess it !

Combinatorics

Contains handwritten notes and text references........

Level 0:

Discrete Mathematics by Kenneth Rosen is too elementary.

Level 1:

Discrete Mathematics for Computer Scientists and Engineers by Stein and Bogart

Discrete Mathematics by Susanna S. Epp

Level 1.5:

Discrete Mathematics For Computer Scientists And Mathematicians by Joe L Mott, Abraham Kandel, Theodore P Baker

Discrete and Combinatorial Mathematics by Ralph Grimaldi

Level 2:

A Path to Combinatorics for Undergraduates: Counting Strategies by Titu Andreescu (BEWARE)

Advanced Combinatorics by Louis Comtet

Level 3:

Concrete Mathematics by Donald Knuth (Don't touch this book...)

Level 4:

Enumerative Combinatorics, Volume 1 by Richard P. Stanley

Enumerative Combinatorics, Volume 2 by Richard P. Stanley

Generating Functionology

Level 5:

Additive Combinatorics by Terence Tao

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Guide to above available materials:

1. The folder named Sigma Notation consist of unpublished notes of Professor H W Gould on Combinatorial Identities. This notes has now been archived in the form of a book.

This is the amazon link:

https://www.amazon.in/Combinatorial-Identities-Stirling-Numbers-Unpublished-ebook/dp/B018DY2B9C/ref=sr_1_1?ie=UTF8&qid=1553097570&sr=8-1&keywords=H+W+Gould

This is the link to the original site:

https://www.math.wvu.edu/~gould/

This book is one of a kind and contains an extensive collection of identities on sums and products found nowhere else on the web. Proofs are left for self derivation for most of the identities. It can serve as a first course for undergrads refering to some topics and the rest are for a more sophisticated course.

2. The folders on P&C and Binomial Theorem will consist of my handwritten notes based on courses which I took, links to online courses, several problem sets and references to "What to read NEXT".

3. Texts on Iversion notation

4. Summation of series by L. B. W. Jolley is an extensive collection of series from algebra, trigonometry and calculus. It is worth looking at and we will be deriving them as we progress with our notes.

5. Derangements-essay and partitions_general-essay are essays from Prof. James Tanton. He deals with high school maths and expresses sophisticated concepts in a manner understandable to non-math audience.

   Link ----> http://www.jamestanton.com/?page_id=20

   Who is he? ----> https://en.wikipedia.org/wiki/James_Tanton

   He has also written a book named Encyclopaedia of Mathematics which sits in my repo "Mathematical Dictionaries, tables and Encyclopaedia" ------> https://github.com/justanotherparadox/Mathematical-Dictionaries-tables-and-Encyclopaedia

6. VVI book summation contains theory of indefinite discrete summations and difference equations as well. We will be dealing with them when I upload my notes in Sequences and Series folder.

7. The book on set theory that I have uploaded is not for a beginner and a lot must be learnt before reading the text. I haven't read it myself and do not feel that I have achieved that level yet.

8. Book by Richard Brualdi and Applied combinatorics (TBC....)